SOLUTION: (1)What does the Principle of Zero Products state? How is it used to solve a quadratic equation? (2)Explain how to complete the square on x2 + 14x. Then write the resulting per

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: (1)What does the Principle of Zero Products state? How is it used to solve a quadratic equation? (2)Explain how to complete the square on x2 + 14x. Then write the resulting per      Log On


   

Question 320743: (1)What does the Principle of Zero Products state? How is it used to solve a quadratic equation?
(2)Explain how to complete the square on x2 + 14x. Then write the resulting perfect square trinomial as the square of a binomial.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) The Principle of Zero Prducts states:
If A*B = 0, then either A = 0, or B = 0, or both A and B are 0.
In solving quadratic equations by factoring, you typically end up with two binomial factors whose product equals zero; for example...
x%5E2%2B25x-84+=+0 and, when factored you get:
%28x-3%29%28x%2B28%29+=+0 Applying the principle of Zero Products, you can state that...
x-3+=+0 or x%2B28+=+0 from which follows...
x+=+3 or x+=+-28
2) To complete the square of x%5E2%2B14x+=+0 you will add the square of half the x-coefficient to both sides of the equation, thus...
x%5E2%2B14x%2B%2814%2F2%29%5E2+=+0%2B%2814%2F2%29%5E2 Simplifying this you get...
x%5E2%2B14x%2B49+=+7%5E2 Factoring the left side gives you...
%28x%2B7%29%5E2+=+7%5E2 which is readily solved by taking the square root of both sides and solving for x.
x%2B7+=+7 or x%2B7+=+-7 so that...
x+=+0 or x+=+-14